The Naked Scientists

The Naked Scientists Forum

Author Topic: Biggest maths fraud in history  (Read 2786 times)

Offline bettybop

  • Jr. Member
  • **
  • Posts: 35
    • View Profile
Biggest maths fraud in history
« on: 01/01/2008 15:20:54 »
Colin leslie dean points out that Godel theorem  is the biggest fraud in
mathematical history
everything dean has shown was known at the time godel did his proof but no
one meantioned any of it ie Godels theorem is invalid as it uses invalid
axioms ie axiom of reducibility

http://gamahucherpress.yellowgum.com/books/philosophy/GODEL5.pdf [nofollow]
look
godel used the 2nd ed of PM he says

Quote
A. Whitehead and B. Russell, Principia Mathematica, 2nd edition,
Cambridge 1925. In particular, we also reckon among the axioms of PM
the
axiom of infinity (in the form: there exist denumerably many individuals),
and the axioms of reducibility
and of choice (for all
types)

note he says he is going to use AR
but
Russell following wittgenstien took it out of the 2nd ed due to it being
invalid NOTE it was not in the 2nd ed which godel used
godel would have know that
russell and wittgenstien new godel used it but said nothing
ramsey points out AR is invalid before godel did his proof
 godel would have know ramseys arguments 
 ramsey would have known godel used AR but said nothing

Quote
Ramsey says

Such an axiom has no place in mathematics, and anything which cannot be
proved without using it cannot be regarded as proved at all.

This axiom there is no reason to suppose true; and if it were true, this
would be a happy accident and not a logical necessity, for it is not a
tautology. (THE FOUNDATIONS OF MATHEMATICS* (1925) by F. P. RAMSEY

every one knew AR was invalid
they all knew godel used it
but nooooooooooooo one said -or has said anything for 76 years untill
dean
the theorem is a fraud the way godel presents it in his proof it is crap


 

Offline bettybop

  • Jr. Member
  • **
  • Posts: 35
    • View Profile
Biggest maths fraud in history
« Reply #1 on: 05/01/2008 11:51:08 »
Russell following wittgenstien took AR  out of the 2nd ed due to it being
invalid NOTE it was not in the 2nd ed which godel used



Where does Russell and  Wittgenstein say this?

http://books.google.com/books?id=I09hCIlhPpkC&pg=PA154&lpg=PA154&dq=taken+out+2nd+ed+principia+russell+axiom+of+reducibility&source=web&ots=DFeWR1-K5M&sig=mc5V4zbVf1y9kxabQePCAOE5zQM" [nofollow]


Quote
]n the Introduction to the second edition of Principia, Russell repudiated Reducibility as 'clearly not the sort of axiom with which we can rest content'

http://links.jstor.org/sici?sici=0029-4624(199306)27%3A2%3C267%3ARR%3E2.0.CO%3B2-H" [nofollow]


Quote
Drawing on the ideas of Wittgenstein, Russell hoped to avoid an axiom of reducibility for elementary number theory


Quote
Ramsey says
 
  Such an axiom has no place in mathematics, and anything which cannot be
  proved without using it cannot be regarded as proved at all.
 
  This axiom there is no reason to suppose true; and if it were true, this
  would be a happy accident and not a logical necessity, for it is not a
  tautology. (THE FOUNDATIONS OF MATHEMATICS* (1925) by F. P. RAMSEY

Where does Godel specifically use it


Quote
(1) Godel uses the axiom of reducibility axiom 1V of his system is the  axiom of reducibility "As Godel says "this axiom represents the axiom of  reducibility (comprehension axiom of set theory)" (K  Godel , On formally undecidable propositions of principia mathematica and  related systems in The undecidable ,  M, Davis, Raven Press, 1965,p.12-13)

    . Godel uses axiom 1V the  axiom of reducibility in his formula 40 where   he states "x is a formula arising from the  axiom schema 1V.1  ((K Godel , On formally  undecidable propositions of principia mathematica and related systems in The undecidable , M, Davis, Raven Press,  1965,p.21

     

    " [40. R-Ax(x) ≡ (∃u,v,y,n)[u, v, y, n <= x & n Var v &  (n+1) Var u & u Fr y & Form(y) & x = u ∃x {v Gen [[R(u)*E(R(v))] Aeq y]}]
   
  x is a formula derived from the  axiom-schema IV, 1 by substitution "

that this is somehow a fraud on Godel's  part?
Russell following wittgenstien took it out of the 2nd ed due to it being
invalid NOTE it was not in the 2nd ed which godel used
godel would have know that
russell and wittgenstien new godel used it but said nothing
ramsey points out AR is invalid before godel did his proof
THEY ALL KNEW IT WAS INVALID AND SAID NOTHING

godel would have know ramseys arguments 
 ramsey would have known godel used AR but said nothing
 

Offline Soul Surfer

  • Neilep Level Member
  • ******
  • Posts: 3345
  • keep banging the rocks together
    • View Profile
    • ian kimber's web workspace
Biggest maths fraud in history
« Reply #2 on: 06/01/2008 09:56:36 »
All mathematicians are terrible pedants.  Whilst I agree that the "proof" of Godel's theorem, that any mathematical or logical structure complicated enough to be interesting will be subject to inconsistencies is itself on shaky ground. The theorem is very probably valid.

Some people fear the fact that in any reasonably well defined system there will always be loopholes and wish to find certainty in everything but that is not our experience of everyday life so why should you expect it.

It is probably quite sensible that the theorem proving this is also of limited certainty so why make all the fuss?
« Last Edit: 06/01/2008 09:59:43 by Soul Surfer »
 

The Naked Scientists Forum

Biggest maths fraud in history
« Reply #2 on: 06/01/2008 09:56:36 »

 

SMF 2.0.10 | SMF © 2015, Simple Machines
SMFAds for Free Forums
 
Login
Login with username, password and session length